1. Field of the Invention
The present invention relates generally to a flux controller for an induction motor and, more particularly, to a flux control apparatus capable of minimizing a decline in flux estimation performance in a low velocity region in a drive inverter system of an induction motor using a sensorless vector control method.
2. Description of the Related Art
Generally, methods for driving an induction motor at variable velocity without using a velocity sensor or a position sensor includes a constant voltage/frequency (VF) control method that is an open loop control method, and a sensorless vector control method that estimates a flux position of a motor rotor from measurements of a voltage, a current, and motor parameters. Since the latter method is excellent in terms of performance for controlling velocity and load variations, the sensorless vector control method has been widely used.
However, the sensorless vector control method is problematic in that voltage required to drive a motor in the low velocity region is reduced, so that voltage (inverter output voltage) inputted into the motor may be erroneously estimated due to offset or dead time, whereby flux estimation performance is deteriorated. Consequently, the sensorless vector control method fails to exhibit sufficient performance in the low velocity region in comparison with a high velocity region.
FIG. 1 is a block diagram illustrating an induction motor system driven at variable velocity by the sensorless vector control method without a velocity (position) sensor.
An inverter 101 outputs voltage to a sensorless induction motor 102 to operate the sensorless induction motor 102 according to a velocity command W*m inputted by a user.
A subtractor 103 calculates a difference between a velocity command W*m inputted from an exterior and an estimated velocity Wm that is one of outputs of a sensorless flux estimator 115, thus detecting a velocity error.
A velocity controller 104 functions to output a current command. Kp—s means a proportional gain, Ki—s means an integral gain, and s means a Laplace operator.
A subtractor 105 calculates a difference between a torque current command i*q and a torque current id to detect a torque current error.
In a torque current controller 106, Kp—q means a proportional gain and Ki—q means an integral gain.
A subtractor 107 calculates a difference between a flux command λ*dr and an estimated flux λdr that is the output of the sensorless flux estimator 115 to detect a flux error.
In a flux controller 108, Kp—f means a proportional gain and Ki—f means an integral gain.
A subtractor 109 calculates a difference between a flux current command i*d and a flux current id to detect a flux current error.
In a flux current controller 110, Kp—d means a proportional gain and Ki—d means an integral gain.
A three-phase converter 111 receives an electric rotating angle θe of a rotor flux of the induction motor 102 from the sensorless flux estimator 115, and converts a torque voltage command V*q that is output of the current controllers 106 and 110 and a flux voltage command V*d into a three-phase voltage command, V*a, V*b and V*c.
A voltage controller 112 includes a power semiconductor device (IGBT), and receives the three-phase voltage command, namely, V*a, V*b and V*c, thus applying three-phase output voltage controlled by the voltage command V*a, V*b and V*c to the induction motor 102 through pulse width modulation (PWM).
Respective current sensors 113a, 113b and 113c are coupled to a three-phase output cable of the voltage controller 112 to detect a three-phase current, ia, ib and ic flowing through the induction motor 102.
A two-phase converter 114 receives a flux angle θe of the rotor of the induction motor 102 and converts a three-phase current of the motor, ia, ib and ic into a torque current iq and a flux current id.
The sensorless flux estimator 115 receives the three-phase current of the induction motor 102 from the current sensor 113a, 113b and 113c, and receives a voltage command from the torque current controller 106 and the flux current controller 110, thus outputting a rotating angle θe of the rotor flux, a magnitude λdr of the rotor flux and a velocity Wm of the motor rotor.
An operation of the above components will be described below in detail. If a user inputs a velocity command W*m for a rotation of the induction motor 102, the subtractor 103 measures a difference between the velocity command W*m and an estimated velocity Wm outputted from the sensorless flux estimator 115 to calculate a velocity error, and inputs the calculated velocity error into the velocity controller 104. The velocity controller 104 calculates a torque current command i*q for rotating the induction motor 102 according to the velocity command W*m, based on the inputted velocity error.
The subtractor 105 measures a difference between the torque current command i*q that is the output of the velocity controller 104 and the torque current iq that is the output of the two-phase converter 114 to calculate a torque current error, and inputs the calculated error into the torque current controller 106.
The torque current controller 106 calculates a torque voltage command V*q for enabling a torque current iq corresponding to the command i*q to flow in the induction motor 102, based on the inputted torque current error.
A subtractor 107 measures a difference between the flux command λ*dr and the flux estimation value λdr inputted from the sensorless flux estimator 115 to calculate a flux error. A value of the flux command λ*dr is previously calculated, and thereafter is stored in a memory unit (not shown) installed in the inverter 101. In equation (1), Vrate and Freqrate are rated voltage and rated frequency of the motor, respectively.
                              λ          *          dr                =                                                            (                2                )                                      ·                          V              rate                                                                                            (                  2                  )                                            ·              2                        ⁢                          π              ·                              Freq                rate                                                                        (        1        )            
The flux controller 108 calculates the flux current command i*d for establishing internal flux of the induction motor 102 according to λ*dr, based on the flux error. The subtractor 109 calculates a flux current error, that is, a difference between the flux current command i*d and the flux current id that is the output of the two-phase converter 114, and transmits the flux current error to the flux current controller 110.
The flux current controller 110 calculates a flux voltage command V*d for enabling a flux current corresponding to the command i*d to flow in the induction motor 102, based on the flux current error. The outputs V*q and V*d of the current controllers 106 and 110 are converted through the three-phase converter 111 into the three-phase voltage command V*a, V*b and V*c and then are inputted into the voltage controller 112.
The three-phase converter 111 receives the torque/flux voltage commands V*q and V*d and the rotating angle θe of the rotor flux of the induction motor 102, and converts the two-phase voltage command of the torque/flux into the three-phase voltage command using equations (2) and (3). In the equations (2) and (3), SIN and COS mean sine and cosine trigonometric functions, respectively.V*ds=−SIN(θe)·V*q+COS(θe)·V*d V*qs=COS(θe)·V*q+SIN(θe)·V*d  (2)V*a=V*ds V*b=−0.5·(V*ds−√{square root over (3)}·V*qs)V*c=−0.5·(V*ds+√{square root over (3)}·V*qs)  (3)
The voltage controller 112 controls output voltage through pulse width modulation to apply voltage V*a, V*b, and V*c from the three-phase converter 111 to the induction motor 102. The three-phase current ia, ib and ic of the induction motor 102 is detected by three current detectors 113a, 113b and 113c, and is converted into the torque current iq and the flux current id via the two-phase converter 114. The two-phase converter 114 converts the three-phase current ia, ib and ic of the motor into the torque current iq that is in proportion to the output torque of the motor and the current id that forms 90 degrees with the torque current and is in proportion to the flux of the motor, using equations (4) and (5). Here, id and iq mean flux/torque current in a synchronous coordinate system, and idss and iqss means flux/torque current in a stationary coordinate system.
                                          ids            S                    =                                                    2                ·                ia                            -              ib              -              ic                        3                          ⁢                                  ⁢                              iqs            S                    =                                    ib              -              ic                                      3                                                          (        4        )                                id        =                                                            SIN                ⁡                                  (                                      θ                    ⁢                                                                                  ⁢                    e                                    )                                            ·                              iqs                S                                      +                                                            COS                  ⁡                                      (                                          θ                      ⁢                                                                                          ⁢                      e                                        )                                                  ·                                  ids                  S                                            ⁢                                                          ⁢              iq                                =                                                    COS                ⁡                                  (                                      θ                    ⁢                                                                                  ⁢                    e                                    )                                            ·                              iqs                S                                      -                                          COS                ⁡                                  (                                      θ                    ⁢                                                                                  ⁢                    e                                    )                                            ·                              ids                S                                                                        (        5        )            
The sensorless flux estimator 115 receives the three-phase current ia, ib and ic of the induction motor 102, an output V*q of the torque current controller 106, an output V*d of the flux current controller 110, and outputs the rotating angle θe of the rotor flux of the induction motor 102, the magnitude λdr of the rotor flux and the velocity Wm of the motor rotor. As shown in FIG. 2, the sensorless flux estimator 115 includes two units therein, that is, a flux estimation unit 202 and a rotating angle and velocity estimation unit 203.
                                          V            *            ds                    =                                                                      -                                      SIN                    ⁡                                          (                                              θ                        ⁢                                                                                                  ⁢                        e                                            )                                                                      ·                V                            *              q                        +                                                            COS                  ⁡                                      (                                          θ                      ⁢                                                                                          ⁢                      e                                        )                                                  ·                V                            *              d                                      ⁢                                  ⁢                              V            *            qs                    =                                                                      COS                  ⁡                                      (                                          θ                      ⁢                                                                                          ⁢                      e                                        )                                                  ·                V                            *              q                        +                                                            SIN                  ⁡                                      (                                          θ                      ⁢                                                                                          ⁢                      e                                        )                                                  ·                V                            *              d                                                          (        6        )                                                      ids            S                    =                                                    2                ·                ia                            -              ib              -              ic                        3                          ⁢                                  ⁢                              iqs            S                    =                                    ib              -              ic                                      3                                                          (        7        )            
When using a stator circuit equation of the induction motor, d-axis (flux axis) and q-axis (torque axis) stator flux estimation values can be obtained as seen from the following equations (8) and (9). In the equations (8) and (9), rs means a stator resistance of the induction motor. A symbol  above the letter used in the equations does not mean an actual measurement value but means an estimation value. Generally, voltage values used in the equations (8) and (9) are not actual measurement values but are command values calculated from the equation (6).{circumflex over (λ)}dss=∫(V*ds−rsidss)ds  (8){circumflex over (λ)}qss=∫(V*qs−rsiqss)ds  (9)
By using a relation between the stator and the rotor of the induction motor based on the stator flux obtained from the equations (8) and (9), rotor flux can be calculated as seen from equations (10) and (11). In the equations (10) and (11), σLs is stator leakage inductance and is given as represented in the equation (12). In the equation (12), Ls is stator inductance of the induction motor, Lr is rotor inductance, and Lm is mutual inductance.
                                          λ            ^                    ds          s                =                                            L              r                                      L              m                                ⁢                      (                                                            λ                  ^                                ds                s                            -                              σ                ⁢                                                                  ⁢                                  L                  s                                ⁢                                  i                  ds                  s                                                      )                                              (        10        )                                                      λ            ^                    qr          s                =                                            L              r                                      L              m                                ⁢                      (                                                            λ                  ^                                qs                s                            -                              σ                ⁢                                                                  ⁢                                  L                  s                                ⁢                                  i                  qs                  s                                                      )                                              (        11        )                                          σ          ⁢                                          ⁢                      L            s                          =                              L            s                    -                                    L              m              2                                      L              r                                                          (        12        )            
The rotor flux calculated using the equations (11) and (12) is supplied to the rotating angle and velocity estimation unit 203, and a rotating angle θe of the rotor flux is calculated as represented in equation (13). In the equation (13), tan−1 is an inverse tangent trigonometric function. According to the kind of a sensorless controller, values of the equation (13) may be applied without correction, or calculation of a phase locked loop (PLL) may be added to the values of the equation (13).
                                          θ            ^                    e                =                              tan                          -              1                                ⁢                                                    λ                ^                            dr              s                                                      λ                ^                            qr              s                                                          (        13        )            
A magnitude λdr of the rotor flux that is one of outputs of the flux estimation unit 201 is calculated as seen from the following equation (14), using the rotor flux of the stationary coordinate system obtained from the equations (11) and (12) and the rotating angle of the equation (13).λdr=COS(θe){circumflex over (λ)}qrs−SIN(θe){circumflex over (λ)}drs  (14)
In the rotating angle and velocity estimation unit 203, the equation (13) is calculated to estimate the rotating angle and the velocity. An electric rotating angle of the flux obtained from the equation (13) is converted into a mechanical rotating angle with a motor pole through the following equation (15). In the equation (15), P denotes an induction motor pole. Further, the current electric rotating angle of the rotor is calculated using the equation (16). Also, the rotor velocity can be more precisely calculated through the phase locked loop. In the equation (16), s denotes a Laplace operator.
                              θ          m                =                              θ            e                    ·                      2            P                                              (        15        )                                          W          m                =                  s          ⁢                                          ⁢                                    θ              m                        .                                              (        16        )            
In order to calculate a result value of the flux and rotating angle estimation unit 203 of the equations (13) to (15), the stator flux of the equations (8) and (9) must be calculated. In such a process, an integral operation is required. However, if the voltage and current values used in the equations (8) and (9) include offset, an integrator leads to a divergence, thus making it difficult to use in practical. Generally, in order to solve such a divergence, a high pass filter is applied to eliminate an influence of a DC (frequency 0) component after the integral operation has been performed as represented in the following equations (17) and (18). In the equations (16) and (17), T denotes a time constant of the high pass filter.
                                          λ            .                    ds          s                =                              Ts                          1              +              Ts                                ⁢                      ∫                                          (                                                      V                    ds                    s                                    -                                                            r                      s                                        ⁢                                          i                      ds                      s                                                                      )                            ⁢                              ⅆ                t                                                                        (        17        )                                                      λ            .                    qs          s                =                              Ts                          1              +              Ts                                ⁢                      ∫                                          (                                                      V                    qs                    s                                    -                                                            r                      s                                        ⁢                                          i                      qs                      s                                                                      )                            ⁢                              ⅆ                t                                                                        (        18        )            
FIG. 3 shows a configuration of the rotating angle and velocity estimation unit 203. This is composed of a rotating angle calculation unit 302 and a velocity calculation unit 303. The rotating angle calculation unit 302 receives the rotor flux of the stationary coordinate system calculated by the equations (17) and (18) from the flux estimation unit 202, and calculates the rotating angle θe of the flux through the inverse trigonometric function of the equation (13).
The velocity calculation unit 303 converts the rotating angle θe of the flux into a mechanical rotating angle and performs a differential, thus obtaining a mechanical rotating velocity Wm of the rotor. In the velocity calculation unit 303, P means a motor pole and is stored in an additional memory unit (not shown).
In the case of driving the induction motor by the sensorless vector control method, a method of obtaining motor flux by performing integral for a back electromotive force of the motor (stator voltage−resistance×current) as used in the equations (8) and (9) has been widely used. Voltage outputted from the inverter to the induction motor is in proportion to a rotating velocity of the motor. Thus, high voltage is required in the case of a high velocity rotation, while low voltage is required in the case of a low velocity rotation. Various analog devices such as the current sensors 113a, 113b and 113c (see FIG. 1) are used to control the inverter. In this process, offset is generally included in the calculated/measured voltage and current.
Since a magnitude of the inverter output voltage is sufficiently greater than that of the offset in a high velocity region having a large back electromotive force, it is possible to perform the integral operation of the equations (8) and (9) without any difficulty. However, in a low velocity region where a back electromotive force is small, so that the magnitude of the inverter output voltage is not sufficiently greater than that of the offset voltage, the operation of the equations (8) and (9) is affected by the offset, thus resulting in the divergence. Hence, it is impossible to use the integral operation of the equations (8) and (9) in practical, and the high pass filter is frequently used together with the integral operation as in the equations (17) and (18) so as to minimize an influence of the offset (frequency 0). In the case of using the high pass filter, the offset of the voltage and current can be overcome. However, the calculation of the equations (17) and (18) is greatly affected by the time constant of the high pass filter. In order to acquire a required flux estimation performance, the time constant of the filter must be sufficiently larger than the rotating velocity of the motor. Therefore, the time constant of the high pass filter must be appropriately selected in consideration of a main operating region of the motor and phase error characteristics of the filter. However, such a method is problematic in that the time constant of the filter must be reduced in a region having a very low frequency, so that it is difficult to expect good flux estimation performance because of the characteristics of the high pass filter such as a phase delay resulting from the reduced time constant.
Further, in the general sensorless vector control, flux is estimated not by real voltage inputted into the motor but by a command voltage of the controller. In the low velocity region where the magnitude of voltage is reduced, an error in voltage caused by dead time affects the estimation of the flux, so that there occurs a difference between command voltage used in the calculation of flux and voltage inputted actually into the motor. The difference leads to an error in the flux estimation.